for \(i=1,\ldots ,N\) .
Here, \(\theta _{i}(t)\in [0,2\pi )\)  is the phase corresponding to \(X_{i}(t)\)  (i.e., the variable obtained from \(X_i(t)\)  via some function \(\mathcal {X}\rightarrow [0,2\pi )\) ) and \(\Gamma _i\)  is the PCF representing effects of the phase differences on the element \(i\)  [1]}.
Note that since the interactions are assumed to be weak, we can approximate the effect only with the phase difference.
